I'm you and you're you

Stranger: Hey
Stranger: Sup, stranger? :d
You: You're stranger...
Stranger: No, you're the stranger, I'm you!
You: No, you're stranger, I'm you, not you!
Stranger: No you're the stranger, I'm you, not you! :o
You: I just said that, Stranger! D<
Stranger: I just said that as well, stranger!
You: I'm you, not you! If you're you and I'm you, then we're both you and thus one person, and that is you.
Stranger: So I'm you after all. >_>
You: No, I'm you... You can't be you if you're you and not me...
Stranger: But you said that so!
Stranger: :O
Stranger: Liar. :<
You: I said that I'm you and you're stranger, but because of the fact that you won't give up that you're you and I'm stranger, then we are both you and not... me... IGNORE MEEE!!!!
Stranger: Weirdo. :p
You: I'll have you know, I do wear two shoes! D<
Stranger: How
Stranger: ...
Stranger: intriguing!
Stranger: Tell me more, please?
You: Eleanor Rigby picks up the rice in a church where a wedding has been.
You: Lives in a dream.
Stranger: Pfft, or don't talk to me, I guess.
Stranger: :<
You: Waits at the window.
Stranger: Now THAT is weird.
Stranger: =P
Stranger: I don't like The Beatles
Stranger: At all. :<
You: WAT.
You: FOOL!
You have disconnected.